#Linear Regression Model

car <- read.csv("CarPrice_Assignment.csv", stringsAsFactors = F)

View(car)
str(car)
summary(car)

# datadictonary
# CarPrice_Assignment data.frame contains 205 obs with 26 variables
# Variables give technical and performance specifications of car models and price
# Variables are of class 'num' , 'int' & 'char'
# Business objective is to foucus on independant variables that have a tight correlation with price of the car

############################################## Data Preparation ##################################################################################

# Checking for duplicate obs in car data.frame

sum(duplicated(car))
sum(duplicated(car$car_ID))

# NIL duplicates found , looking for NAs

sum(is.na(car))

# NIL NAs found

# Categorical variables of 'char' type will be converted to binaries for ease of anlysis

car$fueltype<-as.factor(car$fueltype)
levels(car$fueltype) <- c(1,0)
car$fueltype<-as.numeric(levels(car$fueltype))[car$fueltype]
summary(car$fueltype)

# Checking the number of distinct 'levels' or 'factors' before conversion to binary
# When only two levels are present , variable values can be set to (1,0)

array_name = sqldf("select DISTINCT aspiration from car")
View(array_name)
car$aspiration<-as.factor(car$aspiration)
levels(car$aspiration) <- c(1,0)
car$aspiration<-as.numeric(levels(car$aspiration))[car$aspiration]


array_name = sqldf("select DISTINCT doornumber from car")
View(array_name)
car$doornumber<-as.factor(car$doornumber)
levels(car$doornumber) <- c(1,0)
car$doornumber<-as.numeric(levels(car$doornumber))[car$doornumber]
summary(car$doornumber)

array_name = sqldf("select DISTINCT carbody from car")
View(array_name)

# No.of levels more than two, need to assign dummy values
# create a matrix of dummy variables, convert to data.frame and cbind with main data.frame
# This helps in significance analysis of all possible independent variables

dummy <- data.frame(model.matrix(~ factor(carbody), data=car))
View(dummy)
dummy <- dummy[,-1]
View(dummy)
car1 <- cbind(car[,-7],dummy)
summary(car1)

array_name = sqldf("select DISTINCT drivewheel from car")
View(array_name)
dummy1 <- data.frame(model.matrix(~ factor(drivewheel), data=car1))
dummy1 <- dummy1[,-1]
car2 <- cbind(car1[,-7], dummy1)

array_name = sqldf("select DISTINCT enginelocation from car")
View(array_name)
car2$enginelocation<-as.factor(car2$enginelocation)
levels(car2$enginelocation) <- c(1,0)
car2$enginelocation<-as.numeric(levels(car2$enginelocation))[car2$enginelocation]

array_name = sqldf("select DISTINCT enginetype from car2")
View(array_name)
dummy2 <- data.frame(model.matrix(~ factor(enginetype), data=car2))
dummy2 <- dummy2[,-1]
car3 <- cbind(car2[,-13], dummy2)

array_name = sqldf("select DISTINCT fuelsystem from car3")
View(array_name)
dummy3 <- data.frame(model.matrix(~ factor(fuelsystem), data=car3))
View(dummy3)
dummy3 <- dummy3[,-1]
car4 <- cbind(car3[,-15], dummy3)

# As problem statement, only name of car company is to be retained.
# Car company name is separated as 'brand'

car5 <- separate(car4, CarName, c("brand", "model"), sep = " ")
car5 <- car5[,-4]

# Spell errors in brand names are rectified

car5$brand <- replace(car5$brand, car5$brand=="toyouta", "toyota")
car5$brand <- replace(car5$brand, car5$brand=="vokswagen", "volkswagen")
car5$brand <- replace(car5$brand, car5$brand=="vw", "volkswagen")
car5$brand <- replace(car5$brand, car5$brand=="Nissan", "nissan")
car5$brand <- replace(car5$brand, car5$brand=="porchsce", "porsche")
car5$brand <- replace(car5$brand, car5$brand=="maxda", "mazda")

# Dummy variables created for brand names to analyse significance

dummy4 <- data.frame(model.matrix(~ factor(brand), data=car5))
dummy4 <- dummy4[,-1]
car6 <- cbind(car5[,-3], dummy4)

# Dummy variables for 'symboling'

array_name = sqldf("select DISTINCT symboling from car6")
View(array_name)
dummy5 <- data.frame(model.matrix(~ factor(symboling), data=car6))
dummy5 <- dummy5[,-1]
car7 <- cbind(car6[,-2], dummy5)

# Dummy variables for no.of.cylinders

array_name = sqldf("select DISTINCT cylindernumber from car7")
View(array_name)
dummy6 <- data.frame(model.matrix(~ factor(symboling), data=car7))
dummy6 <- dummy6[,-1]
car8 <- cbind(car7[,-2], dummy6)

# Derived metrics: Average of mpg in city and highway has been taken as a independent variable

car8$avg.mpg <- (car8$citympg+car8$highwaympg)/2
View(car8)
car9 <- car8[,-c(17,18)]

# Carlength has been classified as "Small car" (141-157) , "Midsize" (158-197) & "Luxury" (Above 197)
# Dummy variables et for the three segments

car9$carlength <- as.factor(car9$carlength)
unique(car9$carlength)
levels(car9$carlength)[1:8] <- "smallcar"
levels(car9$carlength)[2:62] <- "midsize"
levels(car9$carlength)[3:8] <- "luxury"
dummy7 <- data.frame(model.matrix(~ carlength, data=car9))
dummy7 <- dummy7[,-1]
car10 <- cbind(car9[,-7],dummy7)

# Variables with just '1' obs have been identified

sum(car9$factor.cylindernumber.twelve)
sum(car9$factor.cylindernumber.three)
sum(car9$factor.fuelsystem.spfi)
sum(car9$factor.fuelsystem.mfi)
sum(car9$factor.enginetype.dohcv)
sum(car9$factor.brand.renault)
sum(car9$factor.brand.mercury)

# Variables with just 1 obs have been discarded as they would be insignificant

car10 <- car10[,-c(22,31,34,43,45,51)]

# CarID discarded as it does not add to price significance

car10 <- car9[,-1]

#### Checking for outliers in numerical variables ##############

ggplot(data=car10, aes(car10$wheelbase)) + geom_histogram( col="red", fill="green", alpha=.2)

quantile(car10$wheelbase, probs = c(0.05,0.95))

quantile(car10$wheelbase,seq(0,1,0.01))

# Capping the outliers at 93-02 and 110.00 beyond whhich there are sharp changes

car10$wheelbase[which(car10$wheelbase>110.00)] <- 110.00

car10$wheelbase[which(car10$wheelbase<93.02)] <- 93.02

# Outliers for enginesize


outlier <- boxplot.stats(car$enginesize)$out

car$enginesize[which(car$enginesize>209.00)] <- 209.00

# Outliers for curbweight

quantile(car10$curbweight,seq(0,1,0.01))

# Sharp changes at 1% and 98% in curbweight capped

carprice$curbweight[which(carprice$curbweight<1819.72)] <- 1819.72
carprice$curbweight[which(carprice$curbweight>3768.40)] <- 3768.40

# Outliers check for carprice

outlier <- boxplot.stats(car10$price)$out

ggplot(data=car10, aes(car10$price)) + geom_histogram( col="red", fill="green", alpha=.2)


# Outlier check for horsepower

ggplot(data=car10, aes(car10$horsepower)) + geom_histogram( col="red", fill="green", alpha=.2)

outlier <- boxplot.stats(car10$horsepower)$out

car10$horsepower[which(car10$horsepower>184.00)] <- 184.00

######################################### Linear Regression Modeling ####################################

#set the seed to 100, let's run it
set.seed(100)

# randomly generate row indices for train dataset
trainindices= sample(1:nrow(car10), 0.7*nrow(car10))

# generate the train data set
train = car10[trainindices,]

#Similarly store the rest of the observations into an object "test".
test = car10[-trainindices,]

# Run the model on the training dataset

model.1 <- lm(price~., data = car10)
summary(model.1)

# Check correlation among all variables

corrs = cor(car10)
View(corrs)

# Run the AIC model steps to examine what variables are insignificant ( '+' sign)

step<-stepAIC(model.1,direction="both")

# Based on inputs from correlation matrix and stepAIC , insignificant variables removed
# Model.2 cleaned of carheight,doornumber,compressionratio,drivewheel,cylindernumber...
# Checked for P-value more than 0.35 , VIF in double-digits

model.2 <-lm(formula=price ~ fueltype + aspiration + enginelocation + carwidth + curbweight +
               enginesize + boreratio + stroke + horsepower + peakrpm +
               factor.carbody.hardtop + factor.carbody.hatchback + factor.carbody.sedan + factor.carbody.wagon +
               factor.enginetype.rotor + factor.brand.audi + factor.brand.bmw + factor.brand.buick + factor.brand.chevrolet +
               factor.brand.jaguar + factor.brand.peugeot + factor.brand.plymouth + factor.brand.porsche +
               factor.brand.saab + factor.brand.toyota + factor.symboling..1 +
               factor.cylindernumber.five + factor.cylindernumber.twelve +
               avg.mpg + carlengthmidsize + carlengthluxury, data = train)
summary(model.2)

# Model.2 has high adjusted R-squared but insignificant variables p-value >0.35

model_3 <-lm(formula=price ~ aspiration + enginelocation + carwidth + curbweight + enginesize + boreratio + stroke +
               horsepower + peakrpm + factor.carbody.hardtop + factor.carbody.hatchback + factor.carbody.sedan +
               factor.carbody.wagon + factor.enginetype.rotor + factor.brand.audi + factor.brand.bmw + factor.brand.buick +
               factor.brand.chevrolet + factor.brand.jaguar + factor.brand.peugeot + factor.brand.porsche + factor.brand.saab +
               factor.symboling..1 + factor.cylindernumber.five  + avg.mpg + carlengthmidsize + carlengthluxury, data = train)
summary(model_3)
vif(model_3)
summary(model_3)

# Model_3 has variables with VIF > 6 and high P-value
# corr check between technically related variables curbweight and engine size

cor(car10$curbweight,car10$enginesize)

# At 0.85 corr, curbweight with higher VIF and P-value has to go

model.4 <- lm(formula=price ~ aspiration + enginelocation + carwidth + enginesize + boreratio + stroke + peakrpm +
          factor.carbody.hardtop + factor.carbody.hatchback + factor.carbody.sedan + factor.carbody.wagon +
          factor.enginetype.rotor + factor.brand.audi + factor.brand.bmw + factor.brand.buick + factor.brand.chevrolet +
          factor.brand.jaguar + factor.brand.peugeot + factor.brand.porsche + factor.brand.saab + factor.symboling..1 +
         factor.cylindernumber.five  + avg.mpg + carlengthmidsize + carlengthluxury, data = train)
summary(model.4)
vif(model.4)
summary(model.4)

# carwidth,enginesize,cylindernumber removed
# Avgmpg though seeming insignificant , domain knowledge prompts retention

model.5 <- lm(formula = price ~ aspiration + enginelocation + boreratio +
     stroke + peakrpm + factor.carbody.hardtop + factor.carbody.hatchback +
     factor.carbody.sedan + factor.enginetype.rotor + factor.brand.audi +
     factor.brand.bmw + factor.brand.buick + factor.brand.chevrolet +
     factor.brand.jaguar + factor.brand.porsche + factor.brand.saab +
     factor.symboling..1 + avg.mpg + carlengthmidsize, data = train)

summary(model.5)
vif(model-5)
summary(model.5)

# Car brands , aspiration,cylindernumber, stroke, bore, rpm, carbodytypes, carwidth, symboling removed for high P-value
# R squared decreased
# enginesize re-introduced

model.10 <- lm(formula=price ~ enginesize + enginelocation + factor.brand.bmw + factor.brand.buick + factor.brand.jaguar
            + avg.mpg + carlengthluxury, data = train)
summary(model.10)
vif(model.10)
summary(model.10)
cor(car10$factor.brand.jaguar, car10$carlengthluxury)

# Corr value luxury removed, carwidth re-introduced to check R-squared

model.11 <- lm(formula=price ~ carwidth+enginesize + enginelocation + factor.brand.bmw + factor.brand.buick +
            factor.brand.jaguar + avg.mpg , data = train)
summary(model.11)
vif(model.11)
summary(model.11)

cor(car10$carwidth,car10$enginesize)
cor(car10$factor.brand.bmw,car10$factor.brand.buick)

# R-Squared improved , corr checked between brands, carwidth/enginesize

model.12 <- lm(formula=price ~ carwidth + enginelocation + factor.brand.bmw + factor.brand.buick +
                 factor.brand.jaguar + avg.mpg , data = train)
summary(model.12)
vif(model.12)
summary(model.12)

# Model.12 with Adj R-Squared 0.9055 and all p-values *** seems good
# Model.11 with Adj R-sqaured 0.9243 and good p-values is the FINAL model.

# Prediction on model.11 will be done on test data

Predict_1 <- predict(model.11,test[,-1])
test$test_price <- Predict_1
r <- cor(test$price,test$test_price)
rsquared <- cor(test$price,test$test_price)^2
rsquared

# Checcking test data with model.12

Predict_4 <- predict(model.12,test[,-1])
test$test_price <- Predict_4
r <- cor(test$price,test$test_price)
rsquared <- cor(test$price,test$test_price)^2
rsquared

# rsquared for model.11 is a decent 0.8555
# Geely can model their car price on significant specifications avg.mpg, carwidth, enginesize
# Geely may closely look at car makers BMW,Buick and Jaguar